Optimization of structural elements

  • Jean-Louis Armand
Optimal Design
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


A numerical method for the solution of structural optimization problems involving ordinary differential equations is presented for a simple situation where the constraint is of an aeroelastic nature. The method is adapted from optimal control theory and has proven successful in a number of structural optimization problems. Its extension to two dimensional structures is outlined ; limitation to situations involving plates, however, is emphasized. It is assumed that the instability exhibited by the optimality condition is related to the fact that plates cannot in general achieve global extrema. Suggestions for further research in this area are presented.


Design Variable Optimal Control Theory Global Extremum Structural Optimization Problem Optimal Structural Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

7. References

  1. Armand, J.L. and W.J. Vitte, (1970), "Foundations of Aeroelastic Optimization and Some Applications to Continuous Systems", Report SUDAAR No 390, Department of Aeronautics and Astronautics, Stanford University, Stanford.Google Scholar
  2. Armand, J.L., (1972), "Applications of the Theory of Optimal Control of Distributed-Parameter Systems to Structural Optimization", NASA CR-2044, June 1972.Google Scholar
  3. Armand J.L., (1973), "Applications of Optimal Control Theory to Structural Optimization: Analytical and Numerical Approach", Proceedings of the IUTAM Symposium on Optimization in Structural Design, Warsaw, Springer-Verlag, Berlin (to be published).Google Scholar
  4. Ashley, Hi. and S.C. McIntosh, Jr., (1968), "Applications of Aeroelastic Constraints in Structural Optimization", Proceedings of the 12 th International Congress of Theoretical and Applied Mechanics, Stanford, Springer-Verlag, Berlin, pp. 100–113.Google Scholar
  5. Bisplinghoff, R.L., Ashley, H. and R.L. Halfman, (1955), "Aeroelasticity", Addison-Wesley Publishing Co., Reading.Google Scholar
  6. Bryson, A.E., Jr. and Y.C. Ho, (1969), "Applied Optimal Control-Optimization, Estimation and Control", Blaisdell Publishing Co., Watham.Google Scholar
  7. Distefano, N., (1974), "Nonlinear Processes in Engineering", Academic Press, New-York.Google Scholar
  8. Dixon, L.C.W., (1967), "Pontryagin's Maximum Principle Applied to the Profile of a Beam", Aeronautical Journal of the Royal Aeronautical Society, 71, pp. 513–515.Google Scholar
  9. Dym, C.L., (1974), "On Some Recent Approaches to Structural Optimization", Journal of Sound and Vibration, 32, pp. 49–70.Google Scholar
  10. Fox, R.L., (1973), "Structural and Mechanical Design Optimization", in Optimization and Design, M. Avriel, M.J. Rijckaert and D.J. Wilde, Eds., Prentice-Hall, Englewood Cliffs, pp. 119–143.Google Scholar
  11. Gallagher, R.H. and O.C. Zienkiewicz, Eds., (1973), Optimum Structural Design: Theory and Applications, John Wiley and Sons, London.Google Scholar
  12. Haug, E.J., Jr., (1969), "Optimal Design of Structural Elements", Lecture Notes, Department of Mechanics and Hydraulics, The University of Iowa, Ames.Google Scholar
  13. Hemp, W.S., (1973), Optimum Structures, Clarendon Press, Oxford.Google Scholar
  14. Lagrange, J.L., (1770–1773), "Sur la Figure des Colonnes", Miscellanea Taurinensia, t.V., in Oeuvres de Lagrange, Tome deuxième, Gauthier-Villars, Paris, 1868, pp. 125–170.Google Scholar
  15. Lurie, K.A., (1963), "The Mayer-Bolza Problem for Multiple Integrals and the Optimization of the Performance of Systems with Distributed Parameters", Applied Mathematics and Mechanics (PMM), Vol. 27, No 5, March 1963, pp. 1284–1299.Google Scholar
  16. Majid, K.I., (1974), Optimum Design of Structures, Newnes-Butterworths, London.Google Scholar
  17. McIntosh, S.C., Jr., (1974), "Structural Optimization via Optimal Control Techniques: A review", Structural Optimization Symposium AMD-VOL. 7, The American Society of Mechanical Engineers, New-York, pp. 49–64Google Scholar
  18. Moe, J. and K.M. Gisvold, (1971), "Optimization and Automated Design of Structures", Report SK/M 21, Division of Ship Structures, Technical University of Trondheim, Trondheim.Google Scholar
  19. Mroz, S., (1973), "Multiparameter Optimal Design of Plates and Shells", Journal of Structural Mechanics, 3, pp. 371–392.Google Scholar
  20. Niordson, F.I., (1965), "On the Optimal Design of a Vibration Beam", Quarterly of Applied Mathematics, 23, pp. 45–53.Google Scholar
  21. Pierson, B.L. and L.J. Genalo, (1974), "Minimum-Weight Design of a Rectangular Flat Panel Subject to a Flutter Speed Constraint", Symposium on Optimization Problems in Engineering and Economics, Naples, Dec. 1974.Google Scholar
  22. Niordson, F.I. and P. Pedersen, (1972), "A Review of Optimal Structural Design", Proceedings of the 13th International Congress of Theoretical and Applied Mechanics, Moscow, Springer-Verlag, Berlin, pp. 264–278.Google Scholar
  23. Olhoff, N., (1973), "On Singularities, Local Optima and Formation of Stiffeners in Optimal Design of Plates", Proceedings of the IUTAM Symposium on Optimization in Structural Design, Warsaw, Springer-Verlag, Berlin (to be published).Google Scholar
  24. Pierson, B.L., (1972), "A survey of Optimal Structural Design Under Dynamic Constraints", International Journal for Numerical Methods in Engineering, 4, pp. 491–499.Google Scholar
  25. Prager, W. and J.E. Taylor, (1968), "Problems of Optimal Structural Design", Journal of Applied Mechanics, 35, pp. 102–106.Google Scholar
  26. Schmit, L.A., Jr., (1971), "Structural Synthesis 1959–1969: A Decade of Progress", in Recent Advances in Matrix Methods of Structural Analysis and Design, R.H. Gallagher, Y. Yamada and J.T. Oden, Eds., The University of Alabama Press, Huntsville, pp. 565–634.Google Scholar
  27. Weisshaar, T.A., (1970), "An Application of Control Theory Methods to the Optimization of Structures Having Dynamic or Aeroelastic Constraints", Report SUDAAR No 412, Department of Aeronautics and Astronautics, Stanford University, Stanford.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Jean-Louis Armand
    • 1
    • 2
  1. 1.Institut de Recherches de la Construction NavaleParisFrance
  2. 2.Ecole PolytechniqueParisFrance

Personalised recommendations